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PDEs and Finite Elements

PDEs and Finite Elements in Mathematica 10

Mathematica Version 10 extends its numerical differential equation-solving capabilities to include the finite element method. Given a PDE, a domain, and boundary conditions, the finite element solution process - including grid and element generation - is fully automated. Stationary and transient solutions to a single PDE or a system of partial differential equations are supported for one, two, and three dimensions.

  • Solve partial differential equations over arbitrarily shaped regions. »
  • Solve stationary and transient PDEs in one, two, and three dimensions.
  • Solve coupled systems of PDEs.
  • Specify Dirichlet boundary conditions. »
  • Specify generalized Neumann and Robin values. »
  • Support for linear PDEs with coefficients that are variable in time and space.
  • Freely formulate coupled PDEs for multiphysics analysis.
  • Specify domains using the full geometric region framework.
  • Fully automatic mesh generation from any region.
  • Obtain solutions as approximate functions that can be further analyzed.
  • Full suite of intermediate-level data structures and solution functions for detailed control and analysis of the solution. »
  • Support for explicit mesh generation.
  • Support for meshes with first- and second-order interpolation.
  • Support for meshes with curved boundaries.

Solve the Telegraph Equation in 1D »
Solve a Wave Equation in 2D »
Solve Axisymmetric PDEs »
Solve PDEs over 3D Regions »

Dirichlet Boundary Conditions »
Neumann Values »
Generalized Neumann Values »
Solve PDEs with Material Regions »

Transient Boundary Conditions »
Transient Neumann Values »
PDEs and Events »
Solve a Complex-Valued Oscillator »

Compute a Plane Strain Deformation »
A Stokes Flow in a Channel »
Structural Mechanics in 3D »
Control the Solution Process »